Radiometer for determining oil film thickness

ABSTRACT

A radiometer is described which coherently detects the thickness of oil films on water by converting continuous-frequency microwave or millimeter-wave brightness temperature versus frequency measurements from the frequency/wavenumber domain to the oil-film-thickness domain (received power versus film thickness).

GOVERNMENT SUPPORT

The Government has rights in this invention pursuant to Contract/GrantNo: 449-4-201, the U.S. Coast Guard Research and Development Center

RELATED U.S. APPLICATIONS

This is a continuation-in-part of application Ser. No. 08/041,728 filedon 1 Apr. 1993, now U.S. Pat. No. 5,381,442.

BACKGROUND OF THE INVENTION

Sea surface oil spills do not spread uniformly, nor without limit. Thickregions having a thickness of a millimeter or more are formed, whichcontain the majority of the oil. Reliable detection of oil thickness isof major importance. A knowledge of the oil distribution, and thelocation of those regions containing the heaviest concentration of oil,would enable the most effective confinement, control and clean-up of theoil.

Multifrequency microwave radiometry has heretofore been employed as atechnique for determining oil thicknesses greater than about 1 mm. ("TheDetermination of Oil Slick Thickness by Means of Multifrequency PassiveMicrowave Techniques", James P. Hollinger, NRL Memorandum Report 2953,June 1974.) This technique is based upon the fact that the apparentmicrowave brightness temperature is different in the region of the oilslick than in the adjacent unpolluted sea by an amount which dependsupon the slick thickness. The oil slick acts as an electromagneticmatching layer between free space and the sea, modulating the brightnesstemperature of the sea. As the thickness of the oil slick is increased,the apparent microwave brightness temperature at first increases andthen passes through alternating maxima and minima, due to the standingwave pattern set up in the film. The adjacent maxima and minima areseparated by integral multiples of a quarter of the electromagneticwavelength in the oil.

Heretofore, the use of microwave radiometry for oil slick thicknessmeasurement has been hindered by several drawbacks in the technology.Chief among these difficulties are the inability to achieve thicknessresolution below about 1 mm and the inability to unambiguously measureoil slicks containing a range of thicknesses.

A need exists, therefore, for an improved microwave radiometer capableof achieving better thickness resolution and having the ability todiscriminate unambiguously different thicknesses of oil contained withina given radiometric antenna pattern.

SUMMARY OF THE INVENTION

In general, the invention is comprised of a radiometer which detects theelectromagnetic energy radiated by a body of water having a film of oilon its surface. The radiometer detects the energy as a brightnesstemperature over a range of radiation frequencies and converts thedetected frequency-domain spectrum to a spectrum of radiation powerversus film thickness. This conversion is accomplished by Fouriertransform signal processing and results in an unambiguous film-thicknessdistribution measurement over a large thickness range.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is an example of a brightness-temperature curve for a uniformoil film of 0.2-cm thickness.

FIG. 1B is an oil-film power spectrum obtained by Fourier transformingthe curve in FIG. 1A from the frequency domain to the thickness domain,in accordance with the invention.

FIG. 2A is a computer generated brightness-temperature curve for an oilfilm containing equal-area patches having 0.1-, 0.2- and 0.4-cmthickness.

FIG. 2B is an oil-film power spectrum obtained by Fourier transformingthe curve in FIG. 2A. The three peaks occur at the associated oil-filmthicknesses.

FIG. 3 is a schematic diagram of a preferred embodiment of theinvention.

DETAILED DESCRIPTION OF THE INVENTION

The electromagnetic power emitted by a large body of water into theatmosphere above it can be estimated by basic principles of radiativetransport theory. In the microwave and millimeter-wavelength spectralregions, the atmosphere is somewhat absorbing because of water vapor anda few other molecular species. Ignoring the atmospheric absorption andemission, we estimate that the power emitted from the water is the sameas that from a blackbody having a temperature equal to the physicaltemperature of the water, T_(W), and an emissivity ε_(W) given byKirchoff's relation 2!, ε_(W) ≈1-r, where r is the radiation reflectancebetween the water and air. The emitted power is thus described by thebrightness temperature, T_(B) ≈εT_(W). In the absence of the oil film,r≈(n_(W) -1)² /(n_(W) +1)², where n_(W) is the refractive index of thewater. Because n_(W) is much greater than 1 in the microwave region, ris close to unity and T_(B) is much less than T_(W).

In the presence of an oil film, the emissivity is modulated by theprocess of multiple-pass interference of radiation in the film. This isa well-known phenomenon in classical optics. Because the refractiveindex of oil, n_(O), in the microwave and millimeter-wave regions ismuch less than that of water, the emissivity can be substantiallyincreased in certain frequency ranges and decreased in others by areduction and enhancement, respectively, in the overall reflectancebetween the water and the air. This is similar to the effect of anintermediate-refractive-index anti-reflection coating on opticalcomponents. For radiation propagating perpendicular to the film, theresult is an overall reflectance of: ##EQU1## where r_(a) and r_(w) arethe reflectances at the oil-air and oil-water interfaces, respectively,t_(a) and t_(w) are the transmittances at the oil-air and oil-waterinterfaces, respectively, k is the free-space wave vector of theradiation, h is the oil-film thickness, and the factor of π in theargument of the cosine accounts for the fact that there is nearly a 180°phase shift upon reflection at the oil-water interface (radiationincident from the oil side).

In the microwave region r_(w) is roughly 0.5 but r_(a) is much closer tozero since r_(a) =(n_(O) -1)² /(n_(O) +1)² and n_(O) is approximately1.5. With this in mind, we can expand Equation 1 with respect to √r_(a)to obtain: ##EQU2## where the identity cos (2n_(o) kh+π)=-cos (2n_(o)kh) has been used.

The brightness temperature is thus approximated by: ##EQU3##

The approximate expression for T_(B) given by Equation 4 can be writtenas:

    T.sub.B ≈T.sub.W (a+b cos 2n.sub.o kh).            (5)

To the extent that the parameters a and b are independent of frequency,the film thickness can be determined uniquely by Fourier transformationof Equation 5 from the wavenumber/frequency domain to the thicknessdomain. This fact is the basis for the signal processing carried out onthick oil films in accordance with the present invention.

To illustrate this signal processing method, we carry out the Fouriercosine transform for a single film of thickness h under the assumptionthat the brightness curve is band-limited from 0 to ω_(max) whereω_(max) =k_(max) c and c is the speed of light in air. In this case,##EQU4## where x is the thickness variable. Substituting in the cosineterm of Equation 5 and evaluating the integral, we find the followingexpression for T_(B) (x): ##EQU5## The first term is a sinc function,defined by sinc(x)=sin(x)/x, that has a peak of unit magnitude atx=2n_(o) h. The second term will be negligible for x>0 provided thatk_(max) (2n_(o) h+x) is greater than or equal to π.

A quantity of great practical importance is the thickness resolution δh.By definition, this is the minimum difference in thickness that two oilfilms can have and still be discriminated in accordance with theinvention. Assuming that only the first term of Equation 7 issignificant, we can define δh using Rayleigh's criterion. This criterionstates that two films of thickness h₁ and h₂, respectively, will be justdiscriminated when the first zero of the sinc function for one film liesat the same x as the peak of the sinc function of the other film.Equivalently, δh is the separation in the thickness domain between thepeak of the sinc function and its first zero. The first zero away fromthe peak is given by ω_(max) (2n_(o) h₁ -x)/c=±π. The separation betweeneither of these zeros and the peak is δx=c/2f_(max). This separationcorresponds to a difference in oil thickness of: ##EQU6## For example,with n_(O) =1.5, we find δh=1.25 and 0.5 mm for f_(max) =40 and 100 GHz,respectively.

To illustrate the Fourier-transform spectroscopy, we first consider auniform film having a thickness of 2 mm and the parameters r_(a) =0.03,r_(w) =0.5, t_(a) =1-r_(a) =0.97, t_(w) =1-r_(w) =0.5 and f_(max) =100GHz. The curve of T_(B) versus f, as calculated from Equation 1, isshown in FIG. 1A under the assumption that T_(W) =280K. As expected, itis quasi-sinusoidal and upon Fourier transformation yields the powerspectrum in FIG. 1B. The side-lobes of the sinc function are adistraction to the eye, but do not affect the correct location of thepeak at h≈0.2 cm. In principle, these side-lobes could be greatlysuppressed by apodizing the T_(B) curve before Fourier transformation.The penalty of apodization is that it increases δh, so that it is not anacceptable procedure when the thickness resolution must be minimized.

A second and more convincing illustration of the Fourier-transformmethod is to consider three separate films of thickness h₁, h₂ and h₃distributed equally within the radiometer beam. Assuming the samereflection and transmission parameters as above and h₁ =1 mm, h₂ =2 mm,and h₃ =4 mm, we obtain the T_(B) curve in FIG. 2A. Because of themixing between the quasi-sinusoidal curves of the three films, thebrightness curve is convoluted. However, the Fourier cosine transformdeconvolves the brightness curve and yields three clearly discerniblepeaks in FIG. 2B at the correct oil-film thicknesses. Of course, adifference in the distribution of the three films would be manifested inthe thickness domain by a difference in the corresponding peakmagnitudes of the power spectrum.

For the measurement of films significantly thinner than about 0.5 mm,existing tecchnology will make it difficult to apply theFourier-transform method. However, Eq. (5) can be applied in a differentway. The idea is to measure the absolute offset in brightnesstemperature of the thin oil film compared to bare water. This offset ΔTis denoted by T_(B) (h)-T_(B) (h=O). In principle, the minimum offsetthat can be measured is approximately ΔT. Making this exact and applyingEq. (5), one finds:

    T.sub.B (h)-T.sub.B (h=0)=ΔT=T.sub.W b(cos 2n.sub.o kh-1)(9)

where b is defined by Eq. (5). Solving for the film thickness, onefinds, ##EQU7## The minimum detectable thickness, h_(min), will beobtained with the maximum k that the radiometer provides. Since k=2π/λ₀,the maximum k corresponds to the minimum λ₀. Therefore, one can write,##EQU8##

As an example, one can use the same parameters applied in the previoussection, λ₀ =3 mm (f_(max) =100 GHz), t_(w) =0.5, r_(w) =0.5, r_(a)=0.03, and n_(o) =1.4. From these values, one finds b=-2t_(w) (r_(a)r_(w))^(1/2) =-0.12 and h_(min) =0.04 mm or 40 microns. This is thinenough to classify as an oil sheen. Oil sheens are of great interest inthe intermediate and latter stages of a large oil spill aftersignificant spreading and weathering have occurred. Oil sheens are alsoof great interest in small spills or leaks that often occur in olderships anchored in harbors or at docks.

Because of limitations on observation time, it is impractical to obtainthe continuous brightness temperature curve of an oil film across anysignificant fraction of the millimeter-wave region (defined as 30 to 300GHz). Therefore, the system of the invention measures the radiation atdiscrete frequencies separated by some frequency interval Δω. ByNyquist's famous sampling theorem, the thickest oil film h_(N) that canbe measured without ambiguity (i.e., without aliasing) is the one whoseT_(B) curve displays one-half cycle over Δω. The so-called Nyquistthickness h_(N) thus satisfies cos2n_(o) Δωh_(N) /c=-1, which leads to:##EQU9## As an example, with n_(O) =1.5 and Δf=1 GHz, we find h_(N) =5cm. The maximum oil-film thickness anticipated in practice is about 1.5cm, so that a 1 GHz interval will easily prevent ambiguity in themeasurement.

To more completely understand the ambiguity problem faced by radiometersprior to the present invention, we assume that T_(B) is measured at onlyone frequency f_(m). Since T_(B) is known for all possible thicknessesat f=0 by the phenomenology discussed above, the effective frequencyinterval in this case is f_(m). This yields a Nyquist thickness ofc/4n_(o) f_(m). For example, a radiometer operating at 40 GHz providesan h_(N) of only 1.25 mm. Any film having thickness greater than orequal to h_(N) will be measured with great ambiguity.

Ideally, the brightness temperature curve should be sampled at roughly1-GHz frequency intervals from zero up to a frequency as high aspractical. From the example given above, an f_(max) of 100 GHz yields athickness resolution of approximately 0.5 mm. In practice, it is verydifficult to obtain complete radiometric data in the band covering 0 to100 GHz because of atmospheric absorption, particularly the H₂ O linenear 22 GHz and the O₂ line near 60 GHz. Other limiting factors are thecomplexity and expense of the instrumentation required to cover such awide frequency range. To alleviate these difficulties, the preferredembodiment of the invention is operated in the two spectral subbandsfrom 26 to 40 GHz and from 75 to 100 GHz. Combined with the knowledge ofT_(B) by default at f=0, the information in the two spectral subbandscan be used to determine the unknown brightness temperature in thefrequency gaps between 0 and 26 GHz and between 40 and 75 GHz byinterpolation. The methods of linear-prediction theory, such asleast-square fitting to polynomials, are well suited for thisinterpolation because T_(B) will be sampled at many frequencies in eachsubband. This will make it possible to interpolate using a polynomial,or some other functional series containing many terms. As a generalrule, the accuracy of the interpolation increases with the number ofterms in the series.

Linear-prediction methods are well suited to digital computers. Theygenerally involve heavy application of techniques in linear algebra,such as matrix manipulation and determinant calculation. Thesetechniques are readily and quickly carried out on digital computersusing any higher-level language that supports multi-dimensional arrays.It is advantageous for the present invention that such computers haverecently advanced to the point that linear prediction methods can becarried out very quickly. For example, microcomputers based on the RISCarchitecture can now carry out linear algebraic calculations at the rateof approximately 10 million floating-point operations per second. Thislevel of computation speed would allow the signal processing associatedwith the present invention to be carried out in real-time or, at worst,pseudo real-time.

Historically, radiometry in the millimeter-wave region has beenconducted primarily by the coherent, or heterodyne detection techniquein a relatively narrow spectral bandwidth equal to roughly 2% of thecenter frequency. The present invention also uses heterodyne detection,but over a very broad frequency range of 30 to 40% of the centerfrequency, The critical function in the heterodyne technique is thedown-conversion of radiation of interest to a much lower frequency wheresignal processing can be readily performed. The down-conversion processoccurs by mixing the incident radiation with the coherent radiation froma local oscillator (LO) to generate a signal at the difference frequency(DF). In the present invention, down-conversion is required for only one(the upper) of the two possible sidebands.

FIG. 3 is a schematic of a preferred embodiment of a Ultra-WidebandRadiometer (UWBR) of the invention, which operates over two widespectral subbands of 26-40 GHz (Subband A) and 75-100 GHz (Subband B).The input beam from a body of water covered with oil is separated intothe subbands by diplexer 12, which may comprise an inductive-meshhigh-pass filter with a cut-on frequency at about 60 GHz.

The mesh filter is mounted at 45° with respect to the input beam.Focusing optics 14a and 14b, placed between the mesh and receiverfeedhorns 16a, 16b, allow the antenna patterns of the two subbandreceivers to be made nearly equal. This is important because thevalidity of interpolating in the frequency gap between 40 and 75 GHzdemands that the T_(B) curves for the two subbands correspond to thesame area on the oil film being observed.

To operate over the wide spectral subbands of 26-40 GHz and 75-100 GHz,the UWBR uses waveguide single-balanced mixers 18a and 18b and fixedfrequency local oscillators 20a and 20b operating just above the cutofffrequency of the waveguide, and a wide DF band containing severalchannels. In both receivers, the down-converted power in each DF band isfrequency demultiplexed into the channels using demultiplexers 22a and22b, amplified in low-noise channel amplifiers, 25a and 25b, square-lawdetected in detectors 24a, 24b, analog averaged in integrators 26a, 26b,digitized by A/D converters 28a, 28b, and then processed by a commoncomputer 30. The frequency interval between channels is chosen to begreat enough to allow for high sensitivity within each channel, but fineenough to provide a Nyquist thickness well above the maximum anticipatedthickness in the oil film. In the preferred embodiment of FIG. 3, thefrequency intervals are 1 and 2 GHz in the 26-40 and 75-100 GHzreceivers, respectively. As shown in the above example, a frequencyinterval of 1 GHz provides a Nyquist thickness of 5 cm. In the typicalsituation, where the oil films have already spread well below 1 cmthickness, the frequency intervals should be increased accordingly. Forexample, the 26-40 GHz subband could be sampled in five channelsseparated by 3-GHz intervals with an h_(N) of approximately 1.7 cm andstill allow for a five-term polynomial or functional series in theinterpolation procedure. The advantages of increasing the frequencyinterval are that the frequency demultiplexer then operates more simplyand effectively and the observation time decreases, as explained below.

The computer 30 processes the digital data from the A-to-D multiplexers28a and 28b by calculating the Fourier transform. There are a number ofstandard computer software packages available that can calculate theFourier transform or, alternatively, custom routines can be written. Ineither case, the transformation is similar algorithmically to the FastFourier Transform first described by Cooley and Tukey in their famouspaper in 1965, "An Algorithm for the Machine Calculation of ComplexFourier Series". The determination of oil film thickness will be carriedout the computer in real time or pseudo real-time as the UWBR collectsdata. The resulting thickness distribution will be displayed andsimultaneously recorded for further analysis and archival purposes.

The sensitivity of the UWBR, like all total-power radiometers, ischaracterized in the microwave and millimeter-wave regions by theminimum detectable temperature ΔT. By definition, this is the brightnesstemperature present at the input to the radiometer that would yield asignal-to-noise ratio of unity after square-law detection and analogaveraging. It is given by: ##EQU10## T_(R) is the receiver noisetemperature, B_(C) is the channel DF bandwidth, τ is the analogintegration time, and C is a constant of order unity, henceforth assumedto equal 1.0. T_(R) is a function of the noise introduced by the DFpreamplifier, losses in the coupling of radiation from the atmosphereinto the mixer, losses in the mixer frequency down-conversion, andlosses in the frequency demultiplexer. In the two proposed subbands ofthe UWBR, the radiation coupling and demultiplexer losses should besmall compared to the mixer single-sideband conversion loss L. In thiscase, one can write:

    T.sub.R ≈T.sub.MIX +LT.sub.DF,                     (14)

where T_(MIX) is the mixer noise temperature and T_(DF) is thepreamplifier noise temperature.

To illustrate these characteristics, we evaluate the expected receiverperformance in the two subbands using components that are availablecommercially. In the 26-40 GHz subband, single-balanced GaAs-basedSchottky-diode mixers manufactured by Watkins-Johnson operate withT_(MIX) ≈800K and L≈6 dB averaged across the band. Room-temperatureGaAs-FET-based DF channel amplifiers made by MITEQ display T_(IF) ≈75K(1.0-dB noise figure) when operating with a channel bandwidth of 1 GHzat center frequencies up to about 12 GHz. Putting this altogether, wefind T_(R) ≈1100K. In the 75-100 GHz subband, another Watkins-Johnsonsingle-balanced mixer typically displays T_(MIX) ≈1500K and L≈8 dBaveraged across the band and the DF channel amplifiers will be the same,so that T_(R) ≈2000K.

Now suppose that we wish to measure T_(B) curves in the two subbandswith 1-GHz wide DF channels and a signal-to-noise ratio of 100. FromFIGS. 1a and 2a, we observe that the average brightness temperature(i.e., the average signal) in the subbands is roughly 130K, so that a ΔTof 1.3K is required from the two receivers. In the 26-40 and 75-100 GHzreceivers, this means that the integration time must be 0.7 and 2.4 ms,respectively.

Although the Fourier transform process is preferred, once the brightnesstemperature spectrum is obtained for a given oil film, there are otherways to transform from the frequency domain to the oil thickness domain.The simplest way is by use of a fitting algorithm. The first step inthis algorithm is to fit the brightness-temperature versus frequencycurve with a polynomial experimentally calibrated curve. The order ofthe polynomial can be as high as the number of data points in the curve.The second step is to fit the data-matched polynomial with an expressionfrom electromagnetic theory. The theoretical expression is based onstanding-wave interference in the oil film, and is readily worked outwith a plane-wave formalism. The thickness of the film is a parameterthat is varied incrementally. The predicted oil-film thickness is thatvalue of the thickness parameter that minimizes the difference betweenthe experiment and the theory in a least-mean-squares sense.

Equivalents

Those skilled in the art will know, or be able to ascertain using nomore than routine experimentation, many equivalents to the specificembodiments of the invention described herein.

These and all other equivalents are intended to be encompassed by thefollowing claims.

The invention claimed is:
 1. A radiometer for determining the thicknessdistribution of an oil film on a body of water comprising:a) a receiverfor detecting the electromagnetic power radiated by the body of waterand oil film by sampling the radiated power over a continuous range offrequencies, and for generating therefrom a first electrical signalproportional to a brightness temperature of the water and film versusradiation frequency; and b) a signal processing means for deriving thethickness distribution of the oil film from the first electrical signal.2. The radiometer of claim 1 wherein the radiated power is coherentlydetected over two subbands, and wherein each subband is within saidcontinuous range of frequencies and comprises an array of channels ofdifferent frequencies and wherein the two subbands comprise a firstsubband extending from about 26 to 40 GHz and a second subband extendingfrom about 75 to 100 GHz.
 3. The radiometer of claim 2 in which thesubband channels are defined by frequency demultiplexers, and eachchannel extends across at least one gigahertz of frequency.
 4. Theradiometer of claim 3 including square-law detectors and integratorscoupled to each channel for generating analog signals proportional tothe sensed brightness temperature in each channel.
 5. The radiometer ofclaim 4 including an analog to digital converter for converting theanalog signals in each channel to digital format, and a digitalmultiplexer for combining the digital signals from each channel.
 6. Theradiometer of claim 1 wherein the signal processing means comprises acomputer.
 7. The radiometer of claim 1 wherein the first signal ismeasured by mixing the radiated power with a local oscillator signal toproduce a signal proportional to the difference between the frequency ofthe radiated power and the local oscillator signal.
 8. The radiometer ofclaim 7 wherein the first signal is divided into a first continuoussubband between about 26-40 GHz and a second continuous subband of about75-100 GHz, and wherein said first and second continuous subbands arewithin said continuous range of frequencies.
 9. The radiometer of claim1 wherein the signal processing means derives the thickness distributionof the oil film by transforming the first signal into a secondelectrical signal, which second electrical signal is proportional toradiative power versus film thickness.
 10. The radiometer of claim 9wherein the signal processing means determines the thickness of the oilfilm by selecting a peak on the radiative power versus film thicknessspectrum and determining the oil film thickness corresponding to thatpeak.
 11. The radiometer of claim 1 wherein the signal processing meansderives the thickness distribution of the oil film by a curve fittingtechnique which compares the first signal to an incremental set ofpredetermined polynomial experimentally calibrated curves.
 12. Theradiometer of claim 11 wherein the signal processing means furtherderives the oil film thickness from the thickness parameter whichminimizes the difference between the experimental curve and the firstsignal by a least-mean-squares technique.
 13. A method for determiningthe thickness distribution of oil film on a body of water comprising thesteps of:a) detecting the electromagnetic power radiated by the body ofwater and oil film over a continuous range of frequencies, andgenerating a first electrical signal therefrom which is proportional toa brightness temperature of the water and film versus radiationfrequency; and b) processing the first electrical signal to obtain athickness distribution of the oil film.
 14. The method of claim 13wherein the radiated power is coherently detected in two subband, saidtwo subbands being within said continuous range of frequencies.
 15. Themethod of claim 14 wherein the two subbands comprise a first subbandextending from about 26 to 40 GHz and a second subband extending from 75to 100 GHz.
 16. The method of claim 15 including dividing the subbandsinto channels, each channel extending across at least one gigahertz offrequency.
 17. The method of claim 16 including generating analogsignals proportional to the sensed brightness temperature of eachchannel.
 18. The method of claim 17 including converting the analogsignals in each subband to digital format and combining the digitalsignals from each subband.
 19. The method of claim 13 wherein the firstelectrical signal is measured by mixing the radiated power with a localoscillator signal to produce a difference proportional to the differencebetween the frequency of the radiated power and the local oscillatorsignal.
 20. The method of claim 19 wherein the first signal is dividedinto a first continuous range of about 26-40 GHz and a second continuousrange of about 75-100 GHz, and wherein said first and second continuousranges are within said continuous range of frequencies.
 21. The methodof claim 13 wherein the step of processing comprises transforming thefirst electrical signal into a second electrical signal, which secondelectrical signal is proportional to radiative power versus filmthickness.
 22. The method of claim 21 further comprising the step ofdetermining the thickness of the oil film by selecting a peak on theradiative power versus film thickness spectrum and determining the oilfilm thickness corresponding to that peak.
 23. The method of claim 13wherein the step of processing comprises comparing the first signal toan incremental set of predetermined polynomial experimentally calibratedcurves using a curve fitting technique.
 24. The method of claim 23further comprising the step of deriving the oil film thickness from thethickness parameter which minimizes the difference between theexperimental curve and the first signal by a least-mean-squarestechnique.
 25. A method of determining the thickness of an oil film on abody of water comprising the steps of:a) forming a power spectrum over apredetermined continuous frequency range of the radiation from the oilfilm and water; b) determining brightness temperature as a function ofradiation frequency over said range; c) transforming the radiationfrequency function to a radiative power versus oil thickness function;and d) selecting radiative power peaks from the radiative power versusoil thickness function and determining the oil film thicknesscorresponding to the peak radiative power.
 26. Apparatus for measuringthe thickness of an oil film on a body of water comprising:a) a receiverfor producing a radiation power versus frequency spectrum of receivedradiation from said body of water over a predetermined continuousfrequency range; and b) a signal processor for converting said spectrumto a brightness temperature versus frequency spectrum and for convertingthe temperature versus frequency spectrum to an oil thickness versusradiative power spectrum, said signal processor selecting radiativepower peaks from the oil thickness versus radiative power spectrum anddetermining oil film thickness corresponding to the peak radiativepower.